A family wants to begin saviving for a trip to paris. The trip is planned for 3 years from now, and the family wants to accumulate one million shillings for the trip, if twelve deposits are made quartely to an account which earns interest at the rate of 8 percent per year compounded quartely, how much should each deposit equal?, How much interest will be earned on their deposits? Urgent please help in next 30min
To find out how much each deposit should equal, we need to use the formula for calculating the future value of an ordinary annuity. The formula is:
FV = PMT * (1 + r)^n * (1 + r)^t
Where:
FV = Future value (in this case, one million shillings)
PMT = Payment amount (the amount of each deposit)
r = Interest rate per period (8% per year divided by 4, since it's compounded quarterly)
n = Number of periods per payment (4, since it's compounded quarterly)
t = Total number of payments (12, since it's made quarterly for 3 years)
Let's plug the values into the formula and solve for PMT:
1,000,000 = PMT * (1 + 0.08/4)^4 * (1 + 0.08/4)^(4*3)
Simplifying the formula:
1,000,000 = PMT * (1.02)^4 * (1.02)^12
1,000,000 = PMT * 1.082432499
Now, divide both sides of the equation by 1.082432499 to solve for PMT:
PMT = 1,000,000 / 1.082432499
PMT ≈ 923,762 shillings
Therefore, each deposit should equal approximately 923,762 shillings.
Now, let's calculate the total amount of interest earned on their deposits:
Total interest earned = (Total amount accumulated - Total amount deposited)
To calculate the total amount accumulated, we use the formula for the future value of an ordinary annuity:
Total amount accumulated = PMT * (1 + r)^n * (1 + r)^t
Total amount accumulated = 923,762 * (1 + 0.08/4)^4 * (1 + 0.08/4)^(4*3)
Total amount accumulated ≈ 1,046,740 shillings
Now, let's subtract the total amount deposited from the total amount accumulated to find the total interest earned:
Total interest earned = 1,046,740 - (923,762 * 12)
Total interest earned ≈ 122,216 shillings
Therefore, the family will earn approximately 122,216 shillings in interest on their deposits.
Please note that these calculations are approximate and may vary slightly due to rounding.